The Elimination of Metrical Heads

stress systems in essentially the same manner as the word serves as a domain for autosegmental operations in grammars that do not utilize feet. Second, the aforementioned Weight-to-Stress Principle is formalized. Third, the Degenerate Foot Principle concerns the interaction of lexical accent with the process of foot-building. Based on data from Mayo, a Uto-Aztecan language of Mexico, it is argued that the presence of a lexical accent linked to any element that is being incorporated into a foot forces that foot to become degenerate. Finally, the Uniform Linking Constraint based on the Uniform Headedness Constraint; see Halle and Vergnaud 1978; Stowell 1979; Hammond 1990b states that all stressed feet within any given word must agree as to which edge the stress autosegment is linked to at all points in the derivation. I begin with a discussion of the formal relationship between stress and metrical structure.

2.1. Defining the Relationship Between Stress and Metrical Structure

This section argues for two distinct claims: i. That the concept of metrical head must be eliminated from phonological theory ii. That feet are always constructed without stress In order to argue that metrical heads are never required, it is first necessary to define what is meant by the term metrical head. Therefore, this section begins with a review of the formal properties that have been attributed to metrical heads. A distinction is drawn between the purely theoretical notion of metrical head and the more descriptive term stress. It is argued that the role of metrical heads is redundant because the latter are always realized as stress, and yet stress may be shown to exist in contexts which arguably lack metrical heads. Next, metrical heads are shown to be absent from the feet that are utilized in prosodic morphology. Finally, I briefly discuss the use of headless feet in the stress system of Yidin y . Having thus argued that the concept of a metrical head lacks empirical motivation, it is concluded that all feet are inherently headless. Next, I address the relationship between stress and feet. Two kinds of evidence are reviewed for the claim that feet are always constructed without stress. The first of these concerns the nature of the feet that are used in prosodic morphology McCarthy and Prince 1986, 1990; Crowhurst 1991b. The second concerns the interaction of metrical structure and stress in Yidin y Halle and Vergnaud 1987b; Hammond 1987b; Crowhurst 1991a; Crowhurst and Hewitt 1995. I turn first to the following questions: what is a metrical head, and is such a concept actually required?

2.1.1. The Elimination of Metrical Heads

The concept of a metrical head, which is sometimes referred to as a strong position, has been utilized quite freely in the study of stress systems. See, for example, Liberman and Prince 1977; Kiparsky 1979; Hayes 1981, 1982a, 1982b, 1987, 1991; Hammond 1985, 1986, 1988a, 1988b, 1990b; Halle and Vergnaud 1987a, 1987b, to name but a few. Nevertheless, very little effort has been devoted to isolating the formal properties of metrical heads. Two notable exceptions to this are Kager 1989 and Crowhurst 1991b. Kager defines a metrical head as a syllable which is the target of Syllable Adjunction, a rule which creates binary metrical feet. 25 Thus, for Kager, a metrical head is defined solely in terms of its role in the rule of Syllable Adjunction. Crowhurst 1991b defines a metrical head in a manner which might seem different from Kager’s but which is, in fact, functionally equivalent to it. Following Hayes 1981, 1982a, 1987, 1991, Crowhurst states that “the metrical head is a constituent required by and dependent on i.e., occurring uniquely within the metrical foot” page 44. Thus, Crowhurst’s theory, like Kager’s, views the head as an obligatory element of a metrical structure. 26 For Crowhurst, that metrical structure is a foot which may or may not be binary, while Kager avoids the term foot but nevertheless creates the equivalent of a binary foot via his rule of Syllable Adjunction. In both theories as well as that of Hayes, a metrical head is entirely dependent upon a metrical foot or the equivalent for its existence. In contrast to the above theories, each of which defines a metrical head as an obligatory element of a metrical structure, I claim that metrical structures are inherently headless. The basic argument for this claim is based on the observation that the presence of the language- particular feature or set of features which we refer to as stress i.e., tone, length, andor volume is the only available diagnostic for the presence of a metrical head. For studies in the phonetics of stress, see Fry 1955, 1958; Lehiste 1970; Liberman 1975; and Pierrehumbert 1980. That is, to my knowledge, no one has ever posited the existence of an abstract metrical head in surface representation apart from the existence of a corresponding non-abstract stress. Furthermore, in those instances where metrical heads are generated at intermediate stages of the derivation in positions which eventually surface without stress, some kind of mechanism must always be invoked by which those metrical heads are deleted. For example, Halle and Vergnaud 1987a, 1987b create the device of conflation for the express purpose of eliminating excess metrical heads. Conflation has the effect of eliminating all but the most prominent metrical head in a representation. Thus, there is no empirical evidence for the existence of metrical heads apart from the existence of stress itself. On the other hand, there are at least two arguments for the existence of stress apart from metrical heads. The first line of reasoning comes from Prince 1983, 1990, who points out that there are many occurrences of stress for which there is arguably no corresponding metrical structure and hence no corresponding metrical head. Prince’s argument focuses on the observation that stress in some languages is assigned to heavy syllables without regard for how close they occur to the edge of the representation. This class of stress system, which Hayes 1981, 1987, 1991 refers to as unbounded quantity sensitive, is 25 As a consequence of this aspect of his theory, Kager proposes the Strict Binarity Hypothesis. My proposal is less strict than Kagers in that I argue for the presence of degenerate feet in certain Mayo words. I differ most significantly from Kager in that I do not require stress to be associated with foot structure; this is explained below. 26 Crowhurst also claims that a metrical head is a template, so that a grammar may require the head to be either bimoraic or monomoraic, independently of the requirements on the foot itself. Crowhurst uses this approach primarily to explain why the feet used in stress systems can sometimes be degenerate while the feet used in morphological processes are always binary. However, Crowhursts arguments for the templatic nature of the head depend crucially upon the assumption that the presence of stress implies the presence of a foot. As Prince 1990 points out, there are arguments against this assumption in unbounded stress systems. Since it is not clear that the foot is independently motivated in the crucial examples that Crowhurst cites as arguing for the templatic nature of the head, I view the latter as an untested hypothesis. exemplified in Khalkha Mongolian, Yana, Aguacatec Mayan, Huasteco, Eastern Cheremis, Komi, Waalubal, Koya and Western Greenlandic Eskimo; each of these is described in Hayes 1981. For example, in Huasteco, the final long vowel of the word gets stressed; if there are no long vowels in a word, then the first vowel is stressed. Representative data are given in 25. 25 Huasteco Larsen and Pike 1949: Øá:šušlom field of garlic k w ahí:lom widow Øalabé:l pretty hu:ßú:kßik blisters bi:nomá:c one who gave e:la:šwá:y they surely find each other cabá:l earth cábal cooked corn Øátem salt cálam shade k w áÖap tarantula hílkomaß leftovers Notice that some of the words in 25 contain sequences of two stressless syllables, and the location of each of these sequences of stressless syllables is determined only by the location of the first long vowel. Because Hayes 1991 assumes the Bijectivity Principle, which claims that there is a one-to-one correspondence between metrical heads and metrical feet, he is forced to conclude from these facts that the grammar of Huasteco as well as the grammars of the other languages mentioned earlier constructs unbounded feet, i.e., feet which may contain any number of syllables. For example, the theory of Hayes 1991 parses Øá:šušlom as a single left- headed foot consisting of three syllables, as illustrated in 26. 26 Øa:šušlom The problem with Hayes’ theory is that unbounded feet, if they exist, should be available to function in templatic morphological processes such as reduplication, just as binary feet have been observed to do. An example of such a process using unbounded feet would be a morphological rule which copies everything up to and including the first heavy syllable of a stem. Since such processes appear to be unattested, I follow Prince in concluding that unbounded feet do not exist. For additional arguments against the existence of unbounded feet, see Hammond 1990b. Instead, I assume that stress assignment is achieved in languages such as Huasteco via the Weight-to-Stress Principle, stated in 27. 27 Weight to Stress Principle Kager 1989; Prince 1990: If heavy, then stressed. The Weight-to-Stress Principle simply means that, in some languages, stress is assigned directly to heavy syllables without the use of feet. Since words which lack heavy syllables are nevertheless stressed on a peripheral syllable in Huasteco as well as in all other languages with unbounded stress, the Weight-to-Stress Principle must be supplemented with the End Rule Prince 1983:73–79. The Weight-to-Stress Principle is discussed and illustrated in sections 2.3.3.2 and 3.2. The point of the above discussion is this: since there is no instance of a morphological process which utilizes unbounded feet, and since unbounded stress systems such as that of Huasteco may be accounted for without feet by appealing to the Weight-to-Stress Principle and the End Rule, I conclude with Prince 1983:73–79, 1990 that unbounded feet do not exist. Consequently, those languages which exhibit unbounded stress instantiate the existence of stress apart from feet. But since feet are not present in unbounded stress systems, then metrical heads, by virtue of their inherent dependence upon feet, cannot be present either. This constitutes the first argument for the existence of stress apart from metrical heads. The second argument is based on the observation that, in many languages such as Spanish Harris 1983, the location of stress is unpredictable in certain words. That is, even though a language may have a set of rules by which stress is normally assigned, there may be some words whose stress patterns are not derivable from those rules. In order to account for the exceptional stress patterns of these words, it is necessary to assume that they have a stress or some element which would derive its exceptional location already present in underlying representation. As an alternative to using lexical stresses henceforth, lexical accents to mark exceptional stress, one might imagine marking an entire foot in underlying representation. This will work for some languages. However, as Michael Hammond personal communication points out, there are a few languages in which exceptional stress can be accounted for only with lexical stresses and not with lexical feet. For example, Macedonian has regular antepenultimate stress as well as a few words which are exceptionally stressed on either the penult or final syllable Lunt 1952; Comrie 1976; Franks 1983; Halle and Vergnaud 1987b; Hammond 1989b. Examples are given in 28. 28 Macedonian Stress: a. Regular Antepenultimate Stress: vodénißar miller vodénißa mill pólkovnik colonel rábota work véßer evening zbór word b. Exceptional Penult and Final Stress: konzumátor consumer literatúra literature komunízam communism autobús bus citát quotation restorán restaurant Comrie 1976 points out that, whenever one or more syllables are suffixed to a word with penultimate stress, it exhibits regular antepenultimate stress. Likewise, whenever one syllable is suffixed to a word with final stress, it exhibits penultimate stress, and following further suffixation it exhibits regular antepenultimate stress. This is illustrated in 29. 27 29 konzumátor konzumátor-i konzumátor-ot konzumatór-ite autobús autobús-i autobús-ot autobús-ite As HV point out, in order to account for regular antepenultimate stress, it is necessary to assume that a final syllable is marked extrametrical by rule except when that syllable bears a lexical accent. Maximally binary, left-stressed syllabic feet are then built from right to left, and all but the rightmost stress is subsequently eliminated via conflation, as shown in 30. Here and henceforth, each stress-bearing unit is represented by an asterisk above the appropriate segment, and stress whether lexical or derived is represented by an additional asterisk placed above the appropriate lower level asterisk. 27 The forms in 28 are basic citation forms, i.e., singular, without article and, for adjectives, masculine gender. In 29, the -i suffix represents plural without an article, the -ot suffix represents singular articulated and the -ite suffix combination represents plural articulated. 30 Underlying: Extrametricality: Build 1st Foot: vodenißa vodenißa vodeni ßa Build 2nd Foot: Build Word Tree: Conflation: Output: . vo deni ßa vo deni ßa vo deni ßa vodénißa In the case of a word with penultimate stress, extrametricality must apply because the final syllable is unaccented. The presence of accent on the penult forces a degenerate foot to be built, as illustrated in 31. 28 31 Underlying: Extrametricality: Build 1st Foot: konzumator konzumator konzuma tor The above analysis produces regular antepenultimate stress in a suffixed form of konzumátor, as illustrated in 32. 32 Underlying: Extrametricality: Build 1st Foot: konzumatori konzumatori konzumato ri Exceptional final stress is derived as follows in 33. 33 Underlying: Extrametricality: Build 1st Foot: autobus Blocked by accent autobus When one or two suffixes are added to a form with final stress, the derivations are the same as in 31 and 32, respectively. Thus, lexical accent is able to account for all of the instances of exceptional stress in Macedonian. There is no way, however, to account for Macedonian exceptional stress in a principled manner if lexical accents are replaced with lexical feet. In particular, suppose a word such as 28 I illustrate only that portion of HV’s analysis which is relevant to the discussion at hand. For the full account of their analysis, see Halle and Vergnaud 1987b:55–56. autobús were represented with an underlying final degenerate foot. Following the addition of two suffixes, such a word would be predicted to have penultimate stress rather than the attested antepenultimate stress. This is illustrated in 34. 34 Underlying: Suffixation: Extrametricality: autobus autobus-ite autobusite Build 1st Foot: Output: autobu si te autobusíte Should be autobúsite The problem in 34 lies in the assumption that an entire foot is present in underlying representation with the added assumption that such a foot cannot expand during the course of a derivation. In contrast, no such problem is encountered when lexical accent is used to represent exceptional stress. I conclude, therefore, that lexical accent is required at least for Macedonian. Thus, exceptional stress in Macedonian instantiates the claim that there are some situations in which a stress is present in the derivation and yet it does not belong to a foot. Another alternative to lexical accent is the use of lexically-specified foot boundaries. This is proposed in Halle 1990 as well as in Halle and Idsardi 1992. However, they use these foot boundaries in a manner that is notationally equivalent to using lexical accent, for they allow only one of a foot’s two boundaries to be underlyingly present in any given representation. The presence of a single foot boundary forces stress to occur on a particular neighboring stress- bearing unit whose location is determined by the setting of the headedness parameter and by whether the lexical boundary is a right or left bracket. Hence, this approach does not constitute the use of underlying feet any more than does a theory which uses lexical accent. The above argument against the use of underlying feet is further supported by the fact that morphological processes should be able to access lexical feet, if they exist, and yet this type of phenomenon has never been reported. In other words, if feet could be present in underlying representation, then we would expect to observe these exceptional feet in morphological processes such as reduplication. The apparent absence of such phenomena supports the claim that all feet are derived by rule. Consequently, idiosyncratic stress has to be attributed to stresses that are present without any corresponding feet in underlying representation. 29 To summarize the foregoing discussion, I have presented two arguments for the existence of stress apart from metrical heads. First, since feet are not present in unbounded stress systems, then metrical heads, by virtue of their inherent dependence upon feet, cannot be present either. Second, the facts of exceptional stress in Macedonian require the use of underlying stresses. 29 Certain aspects of Mayo reduplication in certain words are idiosyncratic. However, chapter 5 argues that these effects are caused by a lexical accent rather than an underlying foot. Underlying feet cannot be used in Macedonian, nor has any morphological evidence been found for the existence of underlying feet. A third argument for the existence of unfooted stresses is based on the superficially complex interaction of stress and length in Mayo. In order to avoid a long digression from the topic at hand, however, the full discussion of these facts is deferred until section 5.2.1.1. Now, given that metrical heads have no phonetic correlate other than stress, and given that stress is not dependent upon the presence of a metrical head, there is no reason to include metrical heads in representations of metrical structure. 30 I conclude, therefore, that metrical heads are redundant and should be eliminated from phonological theory. A potential counter-argument must be addressed at this point. Recall from section 1.2.2 that one of the properties of Hayes’ iambic foot is that its non-head, if it has one, must be light. Recall that all feet have inherent heads in Hayes’ theory. This property, coupled with the requirement that an iambic foot be “right-headed,” means that the foot-building algorithm has to evaluate the weight of each potential “non-head” before it can decide where to place the next foot boundary. For example, if a grammar contains a rule which builds iambs from left to right, then it will parse a string in the following manner. Since “non-heads” always have to be the leftmost member of an iamb, the foot-building rule will begin by examining the weight of the leftmost syllable in the string. If that syllable is light, it will become a “non-head” and the next syllable, regardless of its weight, will become the “head” of that same foot, as illustrated in 35. 35 1st õ Light, 2nd õ Light: 1st õ Light, 2nd õ Heavy: μ μ → μ μ μ μμ → μ μμ If, however, the leftmost syllable is heavy, then it cannot become a “non-head.” Instead, that syllable will be the “head” of a foot and the next syllable will start a new foot regardless of its weight, as shown in 36. 36 1st õ Heavy, 2nd õ Light: 1st õ Heavy, 2nd õ Heavy: μμ μ μ → μμ μ μ μμ μμ μ → μμμμ μ If parsing is from right to left instead of left to right, foot boundaries will still be determined on the basis of the requirement that “non-heads” be light. In this case, the rightmost syllable in the string will become the “head” of a foot regardless of its weight, and 30 Recall from section 1.2.2 that there is some disagreement over the question of whether or not Cairene Arabic exhibits secondary stress. Hayes 1991 claims that metrical heads are attested in all the places where they are predicted by his theory, which includes non-final feet. The basis for this claim comes not from the existence of phonetic features of stress in non-final feet for this is in dispute, but rather from the fact that a “stressless” vowel on the left edge of a foot fails to undergo a phrasal syncope rule which would otherwise apply. If these “metrically strong” vowels should turn out to bear no stress features whatsoever, then they would constitute a potential counter-argument to my claim that metrical heads do not exist. If, however, they exhibit some kind of concrete phonetic features, then they do not constitute a counter-argument to my claim. This question does not appear to be answered in the existing literature on Cairene Arabic stress. the next syllable will be incorporated as the “non-head” of that same foot if and only if it is light; otherwise it will become the “head” of a new foot. 31 37 Final õ Heavy, Penult õ Light: Final õ Heavy, Penult õ Heavy: μ μ μμ → μ μ μμ μ μμ μμ → μ μμ μμ Notice that, regardless of the direction of parsing, it is the “non-head” rather than the “head” which determines where foot boundaries will occur in an iambic foot. What, then, does this reveal about the nature of asymmetric feet? It tells us that asymmetric feet include, as part of their set of defining characteristics, a condition on one of their terminal elements. The specific condition for iambic feet is that the leftmost of two terminal elements be light. This is a condition that is placed on foot-building independently of the placement of stress and, hence, without requiring any reference to the concept of a metrical head. Thus, although it might at first glance appear to be otherwise, Hayes’ definition of the iambic foot does not entail the admission that feet have heads. In conclusion, the theories of Hayes, Kager, and Crowhurst all assume that the metrical head is an obligatory element of a prosodic structure, but I have argued that metrical heads must be eliminated for the following reason. Since stress is the only diagnostic for the presence of a metrical head, it must be the case that one of these entities is unnecessary. Stress cannot be eliminated in favor of metrical heads, for stress can exist independently of metrical structure. This is evidenced by the absence of feet in unbounded stress systems plus the observation that stress, but not metrical structure, can exist in underlying representation. Because of this asymmetric dependency relationship between metrical heads and stress, I consider all feet to be headless. Consequently, feet are henceforth depicted simply as domains in which phonological operations may apply. Section 2.3.3.1 develops the latter claim, which I refer to as the Foot-as-Domain Principle. The foregoing discussion settles the question of whether or not feet have heads, but it also raises the following question: given that stress is not dependent upon metrical structure for its existence, is metrical structure somehow dependent upon stress? That is, can feet exist apart from stress? This question has already been answered by McCarthy and Prince 1990. The next section reviews their arguments.

2.1.2. The Evidence for Stressless Feet